Finite Group Databasebeta

← Group #13165405

Character table — Group #13165405

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122224444444466888888889999121212121212121212121212181818181818181824242424242424242424242424242424363636363636363654545454545472727272
order122236663366666644336666662222444412121212121212124444666612121212121212121212121212121212224412121212444444661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1
χ3111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-111
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ51111111111111111-1-111111111111111111111111111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111-1-111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ81111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ911-1-11-11-111-111-1-1-1i−i111-1-1-11-11-1-11i−i1-1ii−i−i11-1-1ii−i−i11-1-1i−ii−i1-1i−iii−i−i11-1-11-1i−iii−i−ii−i11-1-11-1i−i
χ1011-1-11-11-111-111-1-1-1i−i111-1-1-11-11-1-11i−i-11ii−i−i-1-111−i−iii11-1-1i−ii−i-11i−iii−i−i-1-1111-1−ii−i−iiii−i-1-1111-1−ii
χ1111-1-11-11-111-111-1-1-1i−i111-1-1-11-11-1-11−ii1-1−i−iii11-1-1−i−iii11-1-1i−i−ii1-1i−i−i−iii11-1-1-11i−i−i−iiii−i-1-111-11i−i
χ1211-1-11-11-111-111-1-1-1i−i111-1-1-11-11-1-11−ii-11−i−iii-1-111ii−i−i11-1-1i−i−ii-11i−i−i−iii-1-111-11−iiii−i−ii−i11-1-1-11−ii
χ1311-1-11-11-111-111-1-1-1−ii111-1-1-11-11-1-11i−i1-1ii−i−i11-1-1ii−i−i11-1-1−iii−i1-1−iiii−i−i11-1-1-11−iiii−i−i−ii-1-111-11−ii
χ1411-1-11-11-111-111-1-1-1−ii111-1-1-11-11-1-11i−i-11ii−i−i-1-111−i−iii11-1-1−iii−i-11−iiii−i−i-1-111-11i−i−i−iii−ii11-1-1-11i−i
χ1511-1-11-11-111-111-1-1-1−ii111-1-1-11-11-1-11−ii1-1−i−iii11-1-1−i−iii11-1-1−ii−ii1-1−ii−i−iii11-1-11-1−ii−i−iii−ii11-1-11-1−ii
χ1611-1-11-11-111-111-1-1-1−ii111-1-1-11-11-1-11−ii-11−i−iii-1-111ii−i−i11-1-1−ii−ii-11−ii−i−iii-1-1111-1i−iii−i−i−ii-1-1111-1i−i
χ1722222222222222222222222222-2-2-2-20000000000000000-2-2-2-2220000220000000000000000-2-200000000
χ182222222222222222-2-222222222-2-2-2-20000000000000000-2-2-2-2-2-20000-2-200000000000000002200000000
χ192222-1-1-1-12222222200-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-100222200-1-1-1-1-1-1-1-10000-1-1-1-10000000000
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-1222222-2-2-1-1-1-11111-2-2-2-2-1-1-1-10022-2-200-1-1-1-11111000011110000000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-12222-2-2221111-1-1-1-1-2-2-2-2-1-1-1-100-2-222001111-1-1-1-1000011110000000000
χ222222-1-1-1-12222222200-1-1-1-1-1-1-1-12222-2-2-2-2111111112222-1-1-1-100-2-2-2-200111111110000-1-1-1-10000000000
χ2322-2-22-22-222-222-2-2-22i−2i222-2-2-22-2-222-20000000000000000-2-2222i−2i00002i−2i0000000000000000−2i2i00000000
χ2422-2-22-22-222-222-2-2-2−2i2i222-2-2-22-2-222-20000000000000000-2-222−2i2i0000−2i2i00000000000000002i−2i00000000
χ2522-2-2-11-1122-222-2-2-200-1-1-1111-112-2-222i−2i2-2−i−iii-1-1112i2i−2i−2i-1-111002i−2i2-200−i−iii-1-1110000−i−iii0000000000
χ2622-2-2-11-1122-222-2-2-200-1-1-1111-112-2-222i−2i-22−i−iii11-1-1−2i−2i2i2i-1-111002i−2i-2200−i−iii11-1-10000ii−i−i0000000000
χ2722-2-2-11-1122-222-2-2-200-1-1-1111-112-2-22−2i2i2-2ii−i−i-1-111−2i−2i2i2i-1-11100−2i2i2-200ii−i−i-1-1110000ii−i−i0000000000
χ2822-2-2-11-1122-222-2-2-200-1-1-1111-112-2-22−2i2i-22ii−i−i11-1-12i2i−2i−2i-1-11100−2i2i-2200ii−i−i11-1-10000−i−iii0000000000
χ292-22-22-2-22222-2-22-2-20022-22-2-2-222-22-200000000000000002-2-22000000000000000000000000002i−2i2i−2i0000
χ302-22-22-2-22222-2-22-2-20022-22-2-2-222-22-200000000000000002-2-2200000000000000000000000000−2i2i−2i2i0000
χ312-22-22-2-22222-2-22-2-20022-22-2-2-22-22-220000000000002i−2i2i−2i-222-2000000000000000000002i−2i2i−2i0000000000
χ322-22-22-2-22222-2-22-2-20022-22-2-2-22-22-22000000000000−2i2i−2i2i-222-200000000000000000000−2i2i−2i2i0000000000
χ332-22-2-111-1222-2-22-2-200-1-11-1111-1-22-220000−i3i3−i3i33−33−32i−2i2i−2i1-1-1100000000−i3i3−i3i33−33−30000−ii−ii0000000000
χ342-22-2-111-1222-2-22-2-200-1-11-1111-1-22-220000−i3i3−i3i3−33−33−2i2i−2i2i1-1-1100000000−i3i3−i3i3−33−330000i−ii−i0000000000
χ352-22-2-111-1222-2-22-2-200-1-11-1111-1-22-220000i3−i3i3−i33−33−3−2i2i−2i2i1-1-1100000000i3−i3i3−i33−33−30000i−ii−i0000000000
χ362-22-2-111-1222-2-22-2-200-1-11-1111-1-22-220000i3−i3i3−i3−33−332i−2i2i−2i1-1-1100000000i3−i3i3−i3−33−330000−ii−ii0000000000
χ372-2-2222-2-222-2-2-2-2220022-2-222-2-222-2-200000000000000002-22-2000000000000000000000000002i−2i−2i2i0000
χ382-2-2222-2-222-2-2-2-2220022-2-222-2-222-2-200000000000000002-22-200000000000000000000000000−2i2i2i−2i0000
χ392-2-2222-2-222-2-2-2-2220022-2-222-2-2-2-2220000000000002-2-22-22-22000000000000000000002-2-220000000000
χ402-2-2222-2-222-2-2-2-2220022-2-222-2-2-2-222000000000000-222-2-22-2200000000000000000000-222-20000000000
χ412-2-22-1-11122-2-2-2-22200-1-111-1-111-2-22200003−3−333−3−33-222-21-11-1000000003−3−333−3−3300001-1-110000000000
χ422-2-22-1-11122-2-2-2-22200-1-111-1-111-2-22200003−3−33−333−32-2-221-11-1000000003−3−33−333−30000-111-10000000000
χ432-2-22-1-11122-2-2-2-22200-1-111-1-111-2-2220000−333−33−3−332-2-221-11-100000000−333−33−3−330000-111-10000000000
χ442-2-22-1-11122-2-2-2-22200-1-111-1-111-2-2220000−333−3−333−3-222-21-11-100000000−333−3−333−300001-1-110000000000
χ45444444441-21-21-2-21441-2-211-21-2000000220000222200000000-2-200-1-1110000-1-1-1-10022000000000000-1-1
χ46444444441-21-21-2-21441-2-211-21-2000000-2-20000-2-2-2-200000000-2-20011110000111100-2-200000000000011
χ47444444441-21-21-2-21-4-41-2-211-21-20000002200002222000000002200-1-1-1-10000-1-1-1-100-2-200000000000011
χ48444444441-21-21-2-21-4-41-2-211-21-2000000-2-20000-2-2-2-200000000220011-1-1000011110022000000000000-1-1
χ4944444444-21-21-211-244-211-2-21-2100002200222200000000000011-1-100-2-2-1-1-1-1000022000000000000-1-100
χ5044444444-21-21-211-244-211-2-21-210000-2-200-2-2-2-2000000000000111100-2-211110000-2-20000000000001100
χ5144444444-21-21-211-2-4-4-211-2-21-21000022002222000000000000-1-1-1-10022-1-1-1-10000-2-20000000000001100
χ5244444444-21-21-211-2-4-4-211-2-21-210000-2-200-2-2-2-2000000000000-1-11100221111000022000000000000-1-100
χ534444-2-2-2-24444444400-2-2-2-2-2-2-2-2-4-4-4-4000000000000000022220000000000000000000000000000000000
χ5444-4-44-44-41-2-1-2122-14i−4i1-2-2-1-12120000002-2000022-2-200000000−2i2i00-11i−i0000-1-111002i−2i000000000000−ii
χ5544-4-44-44-41-2-1-2122-14i−4i1-2-2-1-1212000000-220000-2-22200000000−2i2i001-1i−i000011-1-100−2i2i000000000000i−i
χ5644-4-44-44-41-2-1-2122-1−4i4i1-2-2-1-12120000002-2000022-2-2000000002i−2i00-11−ii0000-1-11100−2i2i000000000000i−i
χ5744-4-44-44-41-2-1-2122-1−4i4i1-2-2-1-1212000000-220000-2-222000000002i−2i001-1−ii000011-1-1002i−2i000000000000−ii
χ5844-4-44-44-4-2121-2-1-124i−4i-21122-1-2-100002i−2i002i2i−2i−2i000000000000i−i−ii00−2i2i−i−iii00002-2000000000000-1100
χ5944-4-44-44-4-2121-2-1-124i−4i-21122-1-2-10000−2i2i00−2i−2i2i2i000000000000i−ii−i00−2i2iii−i−i0000-220000000000001-100
χ6044-4-44-44-4-2121-2-1-12−4i4i-21122-1-2-100002i−2i002i2i−2i−2i000000000000−ii−ii002i−2i−i−iii0000-220000000000001-100
χ6144-4-44-44-4-2121-2-1-12−4i4i-21122-1-2-10000−2i2i00−2i−2i2i2i000000000000−iii−i002i−2iii−i−i00002-2000000000000-1100
χ6244-4-4-22-2244-444-4-4-400-2-2-2222-22-444-4000000000000000022-2-20000000000000000000000000000000000
χ634-44-4-222-2444-4-44-4-400-2-22-2222-24-44-40000000000000000-222-20000000000000000000000000000000000
χ644-4-44-2-22244-4-4-4-44400-2-222-2-22244-4-40000000000000000-22-220000000000000000000000000000000000
χ658888-4-4-4-42-42-42-4-4200-122-1-12-12000000440000-2-2-2-2000000000000-2-20000001111000000000000000000
χ668888-4-4-4-42-42-42-4-4200-122-1-12-12000000-4-40000222200000000000022000000-1-1-1-1000000000000000000
χ678888-4-4-4-4-42-42-422-4002-1-122-12-100004400-2-2-2-200000000000000-2-2000011110000000000000000000000
χ688888-4-4-4-4-42-42-422-4002-1-122-12-10000-4-400222200000000000000220000-1-1-1-10000000000000000000000
χ6988-8-8-44-442-4-2-4244-200-12211-2-1-20000004-40000-2-222000000000000-2200000011-1-1000000000000000000
χ7088-8-8-44-442-4-2-4244-200-12211-2-1-2000000-44000022-2-20000000000002-2000000-1-111000000000000000000
χ7188-8-8-44-44-4242-4-2-24002-1-1-2-212100004i−4i00−2i−2i2i2i00000000000000−2i2i0000ii−i−i0000000000000000000000
χ7288-8-8-44-44-4242-4-2-24002-1-1-2-21210000−4i4i002i2i−2i−2i000000000000002i−2i0000−i−iii0000000000000000000000
χ738-88-88-8-882-424-2-44-2002-442-24-2-40000000000000000000000000000000000000000000000000000000000
χ748-88-88-8-88-42-4-242-2400-42-2-44-2420000000000000000000000000000000000000000000000000000000000
χ758-88-8-444-42-424-2-44-200-12-2-11-21200000000000023−2323−2300000000000000000000−33−33000000000000000000
χ768-88-8-444-42-424-2-44-200-12-2-11-212000000000000−2323−2323000000000000000000003−33−3000000000000000000
χ778-88-8-444-4-42-4-242-24002-112-21-2-100000000−2i32i3−2i32i300000000000000000000i3−i3i3−i30000000000000000000000
χ788-88-8-444-4-42-4-242-24002-112-21-2-1000000002i3−2i32i3−2i300000000000000000000−i3i3−i3i30000000000000000000000
χ798-8-8888-8-82-4-24-24-42002-44-22-4-240000000000000000000000000000000000000000000000000000000000
χ808-8-8888-8-8-424-24-22-400-42-24-424-20000000000000000000000000000000000000000000000000000000000
χ818-8-88-4-4442-4-24-24-4200-12-21-121-200000000000023−23−232300000000000000000000−333−3000000000000000000
χ828-8-88-4-4442-4-24-24-4200-12-21-121-2000000000000−232323−23000000000000000000003−3−33000000000000000000
χ838-8-88-4-444-424-24-22-4002-11-22-1-210000000023−23−232300000000000000000000−333−30000000000000000000000
χ848-8-88-4-444-424-24-22-4002-11-22-1-2100000000−232323−23000000000000000000003−3−330000000000000000000000

Here i is the imaginary unit (i² = −1).